Related papers: Chernoff Information between Gaussian Trees
The correlation matrix of massive biomedical data (e.g. gene expression or neuroimaging data) often exhibits a complex and organized, yet latent graph topological structure. We propose a two step procedure that first detects the latent…
Graph Neural Networks (GNNs) have emerged as a flexible and powerful approach for learning over graphs. Despite this success, existing GNNs are constrained by their local message-passing architecture and are provably limited in their…
This paper makes two main contributions: The first is the construction of a near-minimum spanning tree with constant average distortion. The second is a general equivalence theorem relating two refined notions of distortion: scaling…
We study the fundamental question of how likely it is that two randomly chosen trees are isomorphic to each other for different models of random trees. We show that the probability decays exponentially for rooted labeled trees as well as…
Graph neural networks (GNNs) have struggled to outperform traditional optimization methods on combinatorial problems, limiting their practical impact. We address this gap by introducing a novel chaining procedure for the graph alignment…
We study multi-marginal optimal transport (MOT) problems where the underlying cost has a graphical structure. These graphical multi-marginal optimal transport problems have found applications in several domains including traffic flow…
In this work, we study scaling limits of shallow Bayesian neural networks (BNNs) via their connection to Gaussian processes (GPs), with an emphasis on statistical modeling, identifiability, and scalable inference. We first establish a…
A novel Gromov-Wasserstein learning framework is proposed to jointly match (align) graphs and learn embedding vectors for the associated graph nodes. Using Gromov-Wasserstein discrepancy, we measure the dissimilarity between two graphs and…
The Steiner Tree problem is a classical problem in combinatorial optimization: the goal is to connect a set $T$ of terminals in a graph $G$ by a tree of minimum size. Karpinski and Zelikovsky (1996) studied the $\delta$-dense version of…
Graph Neural Networks (GNN) have emerged as a popular and standard approach for learning from graph-structured data. The literature on GNN highlights the potential of this evolving research area and its widespread adoption in real-life…
We investigate the low-dimensional structure of deterministic transformations between random variables, i.e., transport maps between probability measures. In the context of statistics and machine learning, these transformations can be used…
In recommender systems, user-item interactions can be modeled as a bipartite graph, where user and item nodes are connected by undirected edges. This graph-based view has motivated the rapid adoption of graph neural networks (GNNs), which…
This paper looks at the task of network topology inference, where the goal is to learn an unknown graph from nodal observations. One of the novelties of the approach put forth is the consideration of prior information about the density of…
Tree-structured data naturally appear in various fields, particularly in biology where plants and blood vessels may be described by trees, but also in computer science because XML documents form a tree structure. This paper is devoted to…
Graph neural networks are useful for learning problems, as well as for combinatorial and graph problems such as the Subgraph Isomorphism Problem and the Traveling Salesman Problem. We describe an approach for computing Steiner Trees by…
Treewidth is a graph parameter that plays a fundamental role in several structural and algorithmic results. We study the problem of decomposing a given graph $G$ into node-disjoint subgraphs, where each subgraph has sufficiently large…
Employing a recent technology of tree surgery we prove a ``deletion-constriction'' formula for products of rooted spanning trees on weighted directed graphs that generalizes deletion-contraction on undirected graphs. The formula implies…
Many Graph Neural Networks (GNNs) add self-loops to a graph to include feature information about a node itself at each layer. However, if the GNN consists of more than one layer, this information can return to its origin via cycles in the…
Graphical models capture relations between entities in a wide range of applications including social networks, biology, and natural language processing, among others. Graph neural networks (GNN) are neural models that operate over graphs,…
We study the Steiner tree problem on map graphs, which substantially generalize planar graphs as they allow arbitrarily large cliques. We obtain a PTAS for Steiner tree on map graphs, which builds on the result for planar edge weighted…